European Unionchief negotiator Ignacio Garcia Bercero, right, shakes hands Monday with U.S. Assistant Trade Representative for Europe and the Middle East Daniel Mullaney, upon arrival at the European Commission headquarters in Brussels.

BRUSSELS — The United States and the European Union sought Monday to get past a rough patch in diplomatic relations to resume talks on a free trade deal that would grow what is already the world’s biggest business relationship.

Negotiators for the Obama administration and the EU say an agreement would create jobs and boost growth in the two economies, which represent almost half of global output but are still not fully recovered from recession. The trade volume in goods and services between the two economies totaled $1.08 trillion last year.

The negotiations, however, are taking place against the backdrop of European pique over reported U.S. electronic espionage of EU citizens, including high-profile leaders like Germany’s Angela Merkel. The Greens in the European Parliament on Monday became the latest political group to call for the trade talks to be frozen in response.

Concerns over the talks also grew last week when a Belgian court accused the EU’s top trade official of tax fraud. European Commission spokeswoman Pia Ahrenkilde Hansen assured reporters Monday that Karel De Gucht’s legal troubles “will not have any impact” on the talks.

But both European and U.S. officials have said the benefits of the proposed Transatlantic Trade and Investment Partnership are too great to let other issues jeopardize them. The weeklong bargaining session in Brussels, which was delayed due to the U.S. government shutdown, was expected to discuss services, investment, energy and raw materials, and regulatory issues.

A deal could include a reduction in tariffs. But negotiators say the biggest boon, to business and consumers alike, could come from trimming the red tape that often makes it difficult to buy and sell across the Atlantic.

One European study has found that dealing with regulations and bureaucracy on the other side of the ocean can add 10 percent to 20 percent to the price of an imported item, like a car. TTIP could make it possible for a vehicle deemed safe for sale in Europe to be sold in the United States, or vice versa, without additional tests or adaptations being needed.

According to a study co-sponsored by the Atlantic Council, a Washington-based think tank, TTIP could create as many as 750,000 jobs in the United States. The European Commission estimates it would inject $161 billion yearly into the economy of the 28-nation trade bloc, and lead to hundreds of thousands of new jobs.

“The TTIP would be the cheapest stimulus package imaginable,” the European Commission’s Directorate-General for Trade said in a report.

Frances Burwell, the Atlantic Council’s director of Transatlantic Relations and Education Programs, said that as well as administering a welcome jolt to the American and European economies, TTIP could establish health and safety rules that would become standard not just for America and Europe, but for China and other rising economic powers.

“If you look forward, the U.S. and Europe in 20 years will be a smaller part of the global economy. We need to figure out ways to stay competitive,” Burwell said an interview. “And also we need to figure out ways to reinforce the rules that have helped us to be competitive and protect the safety and security of our citizens in terms of the goods they buy, the foods they eat.”

A first round of TTIP talks was held in Washington in July. Negotiators will return there the week of Dec. 16. At a minimum, the Europeans are hoping to announce results in some areas by 2014.